Let $S$ be a commutative ring with topologically noetherian spectrum, and let $R$ be the absolutely flat approximation of $S$. We prove that subsets of the spectrum of $R$ parametrise the localising subcategories of $mathsf{D}(R)$. Moreover, we prove the telescope conjecture holds for $mathsf{D}(R)$. We also consider unbounded derived categories of absolutely flat rings that are not semi-artinian and exhibit a localising subcategory that is not a Bousfield class and a cohomological Bousfield class that is not a Bousfield class.
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机译：令$ S $为具有拓扑Noether谱的交换环，令$ R $为$ S $的绝对平坦近似值。我们证明了$ R $参数的频谱子集是$ mathsf {D}（R）$的本地化子类别。此外，我们证明了望远镜猜想对于$ mathsf {D}（R）$成立。我们还考虑了绝对平环的无界派生类别，这些类别不是半artinian的，并且显示的本地化子类别不是Bousfield类，而同调的Bousfield类不是Bousfield类。
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